Difference between revisions of "1995 USAMO Problems/Problem 4"
Euler brick (talk | contribs) (Created page with "Suppose <math>q_1,q_2,...</math> is an infinite sequence of integers satisfying the following two conditions: (a) <math>m - n </math> divides <math>q_m - q_n</math> for <math>m>...") |
(Reconstructed from page template) |
||
| Line 1: | Line 1: | ||
| + | ==Problem== | ||
Suppose <math>q_1,q_2,...</math> is an infinite sequence of integers satisfying the following two conditions: | Suppose <math>q_1,q_2,...</math> is an infinite sequence of integers satisfying the following two conditions: | ||
| Line 6: | Line 7: | ||
Prove that there is a polynomial <math>Q</math> such that <math>q_n = Q(n)</math> for each <math>n</math>. | Prove that there is a polynomial <math>Q</math> such that <math>q_n = Q(n)</math> for each <math>n</math>. | ||
| + | |||
| + | ==Solution== | ||
| + | {{solution}} | ||
| + | |||
| + | ==See Also== | ||
| + | {{USAMO box|year=1995|num-b=3|num-a=5}} | ||
| + | {{MAA Notice}} | ||
| + | [[Category:Olympiad Algebra Problems]] | ||
Revision as of 07:07, 19 July 2016
Problem
Suppose 
is an infinite sequence of integers satisfying the following two conditions:
(a) 
divides 
for 
(b) There is a polynomial 
such that 
for all 
.
Prove that there is a polynomial 
such that 
for each .
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See Also
| 1995 USAMO (Problems • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 | ||
| All USAMO Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
